Since 128kbit/s MP3s usually has a low-pass filter at 16,000 Hz, and the Nyquist-Shannon theorem states that all frequencies under f/2 Hz can be totally described at an f Hz sampling rate, why not encode at 32,000 Hz? Wouldn't it save more space?

Since 128kbit/s MP3s usually has a low-pass filter at 16,000 Hz, and the Nyquist-Shannon theorem states that all frequencies under f/2 Hz can be totally described at an f Hz sampling rate, why not encode at 32,000 Hz? Wouldn't it save more space?

Since encoding happens in the frequency domain anyway, there isn't much savings. It'll just not encode those frequencies, which is pretty close to downsampling, but much easier to implement.

and this duration can be divided into three short blocks of 192 samples each (and a third of the duration) to handle transients with greater time resolution for the same bitrate at the expense of worse frequency resolution for the same bitrate (very high bitrate overcomes this, but you're talking about CBR)